55:148 Digital Image Processing Chapter 11 3D Vision, Geometry Topics: Basics of projective geometry Points and hyperplanes in projective space Homography.

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55:148 Digital Image Processing Chapter 11 3D Vision, Geometry Topics: Basics of projective geometry Points and hyperplanes in projective space Homography Estimating homography from point correspondence The single perspective camera An overview of single camera calibration Calibration of one camera from the known scene Scene reconstruction from multiple views Triangulation Projective reconstruction Matching constraints Bundle adjustment Two cameras, stereopsis The geometry of two cameras. The fundamental matrix Relative motion of the camera; the essential matrix Estimation of a fundamental matrix from image point correspondences Camera Image rectification Applications of the epipolar geometry in vision Three and more cameras Stereo correspondence algorithms

Fundamental matrices relating multiple cameras

Image rectification (before)

Image rectification (after)

Image rectification What happens in terms of epipolar geometry? Where are the two epipoles What is relation between baseline and image and the camera matrices Can we solve it using a homographic transformation on each cameral image?

Image rectification What happens in terms of epipolar geometry? Where are the two epipoles What is relation between baseline and image and the camera matrices Can we solve it using a homographic transformation on each cameral image?

Image rectification: advantages 3D reconstruction becomes easier Image stitching to generate panoramic views a b c

Panoramic view

So, how to accomplish image rectification? Learn how to determine the fundamental matrix Relative camera motion and essential matrix Relation between fundamental matrix and camera matrix Compute image rectification

Computation of the fundamental matrix using point correspondence Number of unknowns: